Graph of the Inverse Cosine Function

$\cos^{-1}:[-1,1]\to[0,\pi]$ receives $x\in[-1,1]$ and returns $y\in[0,\pi]$. As $x$ increases from $-1$ to $1$, $y$ DECREASES from $\pi$ to $0$ — inverse cosine is a strictly DECREASING, continuous curve, shown in Fig. 4.14.

Equivalently, Fig. 4.14 is obtained by reflecting the restricted cosine curve Fig. 4.12 (on $[0,\pi]$) in the line $y=x$, illustrated against the reflection line in Fig. 4.13.

Notes.

1. The graph is also obtained from $y=\cos x$ by interchanging the $x$- and $y$-axes.
2. For $y=\cos^{-1}x$: the $x$-intercept is $1$ (since $\cos^{-1}(1)=0$) and the $y$-intercept is $\tfrac{\pi}2$ (since $\cos^{-1}(0)=\tfrac{\pi}2$). …